DOCSLIB.ORG

Median, Mode, and Range

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Median, Mode, and Range 5.5 Median, Mode, and Range Describe situations in real life where the mean STATES is not a good representation of the average. STANDARDS MA.6.S.6.1 1 ACTIVITY: Comparing Three Samples Work with a partner. Surveys are taken in three grade 6 –12 schools in Florida. Make up a story about the three surveys. Find the mean for each survey. Do you think the mean is a good way to represent the “average” of each group? Why or why not? a. 1112 13 14 15 16 17 18 b. 1112 13 14 15 16 17 18 c. 1112 13 14 15 16 17 18 216 Chapter 5 Ratios, Rates, and Data Analysis 2 ACTIVITY: When the Mean is Misleading Work with a partner. Read and re-read each statement. Think of a better way to represent the “average” so that the statement is not so misleading. a. Someone is trying to criticize a small high school by saying Age of Graduating Class “Last year, the average age of the 12 graduating class was 22 years old.” 10 When you look into the facts, you 8 fi nd that the class had a senior citizen who went back to school to 6 earn a diploma. Here are the ages 4 for the class. 2 18, 18, 18, 18, 18, 17, 18, 0 Number of Graduates 74 19, 18, 18, 18, 18, 18, 74 17 19 18 Age of Graduates What percent of the ages are below the mean? b. There is a small town where Families’ Yearly Income most of the people are having a diffi cult time getting by because 5 of low incomes. Someone is trying to ignore the problem and writes 4 an article in the newspaper saying “It is not so bad in the 3 town. The average income for a family is $52,000 a year.” Here 2 are the incomes. $20,000, $20,000, $20,000, Number of Families $20,000, $30,000, $30,000, 1 $30,000, $30,000, $40,000, 0 $40,000, $40,000, $50,000, 50,000 310,000 20,000 $50,000, $50,000, $310,000 30,000 40,000 What percent of the families have Yearly Income (dollars) incomes below the mean? 3. IN YOUR OWN WORDS Describe situations in real life where the mean is not a good representation of the average. What measures (other than mean) can you use to describe an average? Use what you learned about the mean to complete Exercises 5 and 6 on page 220. Section 5.5 Median, Mode, and Range 217 5.5 Lesson Lesson Tutorials A measure of central tendency is a measure that represents the center of Key Vocabulary a data set. The mean is one type of measure of central tendency. Here are measure of central two others. tendency, p. 218 median, p. 218 mode, p. 218 range, p. 219 Median Words Order the data. For a set with an odd number of values, the median is the middle value. For a set with an even number of values, the median is the mean of the two middle values. Numbers Data: 5, 8, 9, 12, 14 The median is 9. Data: 2, 3, 5, 7, 10, 11 5 + 7 The median is — , or 6. Study Tip 2 The mode is the only measure of central Mode tendency that can be Words The mode of a data set is the value or values that occur most used to describe a set often. Data can have one mode, more than one mode, or no of data that is not made mode. When all values occur only once, there is no mode. up of numbers. Numbers Data: 11, 13, 15, 15, 18, 21, 24, 24 The modes are 15 and 24. EXAMPLE 1 Finding the Median and Mode Find the median and mode of the bowling scores. Bowling Scores 120 135 160 125 90 90, 105, 120, 125, 135, 145, 160, 160, 175, 205 Order the data. 205 160 175 105 145 135 + 145 280 Median: — = — , or 140 Add the two middle values and divide by 2. 2 2 Mode: 90, 105, 120, 125, 135, 145, 160, 160, 175, 205 The value 160 occurs most often. The median is 140. The mode is 160. Find the median and mode of the data. 1. 20, 4, 17, 8, 12, 9, 5, 20, 13 2. 100, 75, 90, 80, 110, 102 218 Chapter 5 Ratios, Rates, and Data Analysis EXAMPLE 2 Finding the Mode The list shows the favorite types of movie for students in a class. Favorite Types of Movies Organize the data in a frequency table. Then fi nd the mode. Comedy Drama Horror Type Tally Frequency Horror Drama Horror ∣̇∣̇∣̇∣̇∣ ̇ The number of tally Comedy Comedy Action Action ̇̇̇̇ 5 ∣̇∣̇∣̇∣̇∣ ̇∣̇∣̇∣ marks is the frequency. Action Comedy Action Comedy ̇̇̇̇ ̇̇̇ 8 ̇∣̇∣̇∣̇∣ Horror Drama Comedy Drama ̇̇̇̇ 4 ∣̇∣̇∣̇∣̇∣ ̇∣̇∣ Comedy Comedy Horror Horror ̇̇̇̇ ̇̇ 7 Horror Comedy Action Make a tally for each vote. Horror Action Drama Comedy received the most votes. So, the mode is comedy. 3. In Example 2, one member of the class was absent and Exercises 7–15 ends up voting for horror. Does this change the mode? Explain. The range of a data set is the difference between the greatest value and the least value. The range describes how spread out the data are. EXAMPLE 3 Standardized Test Practice Record Length The table shows the record lengths of the six venomous Snake (inches) snakes found in Florida. What is the range of the lengths? Copperhead 53 ○A 43.5 inches ○B 48.5 inches Cottonmouth 74.5 ○C 65 inches ○D 74.5 inches Diamondback 96 rattlesnake 31, 47.5, 53, 74.5, 74.5, 96 Order the dataata fromfrom least to greatest.gr Timber rattlesnake 74.5 The least value is 31. The greatestt Pygmy rattlesnake 31 value is 96. So, the range is 96 − 31,1, Coral snake 47.5 or 65 inches. The correct answer is ○C . 4. The data set shows how many inches of rain fell in several cities during a storm. 3.9, 4.25, 4.1, 3.7, 3.8, 4.3, 3.8, 4.5 Find the range of the data. Section 5.5 Median, Mode, and Range 219 5.5 Exercises Help with Homework 1. NUMBER SENSE Give an example of a data set that has no mode. 2. WRITING Which is affected more by an outlier: the mean or the median? Explain. 3. REASONING What two data values do you need to know to fi nd the range? Explain. 4. NUMBER SENSE A data set has a mean of 7, a median of 5, and a mode of 8. Which of the numbers 7, 5, and 8 must be in the data set? Explain. 6)=3 9+(- )= +(-3 3 9)= 4+(- 1)= 9+(- Find the mean of the data. Is the mean a good “average”? If not, what would be a better “average”? Explain. 5. 8, 29, 30, 30, 30 6. 16, 24, 13, 66, 22, 26, 22, 28 Find the median, mode(s), and range of the data. 1 3 7. 3, 5, 7, 9, 11, 3, 8 8. 14, 19, 16, 13, 16, 14 9. 93, 81, 94, 71, 89, 92, 94, 99 10. 44, 13, 36, 52, 19, 27, 33 11. 12, 33, 18, 28, 29, 12, 17, 4, 2 12. 55, 44, 40, 55, 48, 44, 58, 67 13. ERROR ANALYSIS Describe and correct the error in fi nding the median and range of the data. ✗ The median is 58. 63, 55, 49, 58, 50, 59, 51 The range is 63 − 51, or 12. Find the mode(s) of the data. 2 14. Shirt Color 15. Talent Show Acts Black Blue Red Singing Dancing Comedy Pink Black Black Singing Singing Dancing Gray Green Blue Juggling Dancing Singing Blue Blue Red Singing Poetry Dancing Yellow Blue Blue Comedy Magic Dancing Black Orange Black Poetry Singing Singing Black 16. REASONING In Exercises 14 and 15, can you fi nd the mean and median of the data? Explain. 17. REASONING How does an outlier affect the range of a data set? Explain. 220 Chapter 5 Ratios, Rates, and Data Analysis 18. SUPREME COURT The data show the years of service of the justices of the Supreme Court as of 2008. Find the mean, median, mode(s), and range of the data. 2, 14, 15, 20, 3, 22, 18, 33, 17 Find the mean, median, mode(s), and range of the data. 19. 5, 13, 24, 28, 5, 19, 20, 16, 0, 19 20. 77, 73, 75, 78, 79, 72, 74, 68, 81, 83, 76 1 5 1 3 5 1 5 1 21. 4.7, 8.51, 6.5, 7.42, 9.64, 7.2, 9.3 22. 8 — , 6 — , 3 — , 5 — , 6 — , 5 — , 10 — , 4 — 2 8 8 4 8 4 8 2 Little League Team 23. BASEBALL Find the median, mode, and range 8 of the ages of players on the Little League team. 7 Explain how you found your answers. 6 24. HOMEWORK 5 Write down the number of 4 minutes you spent on homework each day 3 of the past week. 2 a. Find the mean, median, mode(s), and Number of Players 1 0 range of the data. 10 11 12 Age b. How do you think your success as a student is related to the median of your data? the mode? the range?g 25.
Load more

Recommended publications
  • Concentration and Consistency Results for Canonical and Curved Exponential-Family Models of Random Graphs
    CONCENTRATION AND CONSISTENCY RESULTS FOR CANONICAL AND CURVED EXPONENTIAL-FAMILY MODELS OF RANDOM GRAPHS BY MICHAEL SCHWEINBERGER AND JONATHAN STEWART Rice University Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple example of a random graph with additional structure is a random graph with neighborhoods and local dependence within neighborhoods. We develop the first concentration and consistency results for maximum likeli- hood and M-estimators of a wide range of canonical and curved exponential- family models of random graphs with local dependence. All results are non- asymptotic and applicable to random graphs with finite populations of nodes, although asymptotic consistency results can be obtained as well. In addition, we show that additional structure can facilitate subgraph-to-graph estimation, and present concentration results for subgraph-to-graph estimators. As an ap- plication, we consider popular curved exponential-family models of random graphs, with local dependence induced by transitivity and parameter vectors whose dimensions depend on the number of nodes. 1. Introduction. Models of network data have witnessed a surge of interest in statistics and related areas [e.g., 31]. Such data arise in the study of, e.g., social networks, epidemics, insurgencies, and terrorist networks. Since the work of Holland and Leinhardt in the 1970s [e.g., 21], it is known that network data exhibit a wide range of dependencies induced by transitivity and other interesting network phenomena [e.g., 39]. Transitivity is a form of triadic closure in the sense that, when a node k is connected to two distinct nodes i and j, then i and j are likely to be connected as well, which suggests that edges are dependent [e.g., 39].
    [Show full text]
  • Use of Statistical Tables
    TUTORIAL | SCOPE USE OF STATISTICAL TABLES Lucy Radford, Jenny V Freeman and Stephen J Walters introduce three important statistical distributions: the standard Normal, t and Chi-squared distributions PREVIOUS TUTORIALS HAVE LOOKED at hypothesis testing1 and basic statistical tests.2–4 As part of the process of statistical hypothesis testing, a test statistic is calculated and compared to a hypothesised critical value and this is used to obtain a P- value. This P-value is then used to decide whether the study results are statistically significant or not. It will explain how statistical tables are used to link test statistics to P-values. This tutorial introduces tables for three important statistical distributions (the TABLE 1. Extract from two-tailed standard Normal, t and Chi-squared standard Normal table. Values distributions) and explains how to use tabulated are P-values corresponding them with the help of some simple to particular cut-offs and are for z examples. values calculated to two decimal places. STANDARD NORMAL DISTRIBUTION TABLE 1 The Normal distribution is widely used in statistics and has been discussed in z 0.00 0.01 0.02 0.03 0.050.04 0.05 0.06 0.07 0.08 0.09 detail previously.5 As the mean of a Normally distributed variable can take 0.00 1.0000 0.9920 0.9840 0.9761 0.9681 0.9601 0.9522 0.9442 0.9362 0.9283 any value (−∞ to ∞) and the standard 0.10 0.9203 0.9124 0.9045 0.8966 0.8887 0.8808 0.8729 0.8650 0.8572 0.8493 deviation any positive value (0 to ∞), 0.20 0.8415 0.8337 0.8259 0.8181 0.8103 0.8206 0.7949 0.7872 0.7795 0.7718 there are an infinite number of possible 0.30 0.7642 0.7566 0.7490 0.7414 0.7339 0.7263 0.7188 0.7114 0.7039 0.6965 Normal distributions.
    [Show full text]
  • Synthpop: Bespoke Creation of Synthetic Data in R
    synthpop: Bespoke Creation of Synthetic Data in R Beata Nowok Gillian M Raab Chris Dibben University of Edinburgh University of Edinburgh University of Edinburgh Abstract In many contexts, confidentiality constraints severely restrict access to unique and valuable microdata. Synthetic data which mimic the original observed data and preserve the relationships between variables but do not contain any disclosive records are one possible solution to this problem. The synthpop package for R, introduced in this paper, provides routines to generate synthetic versions of original data sets. We describe the methodology and its consequences for the data characteristics. We illustrate the package features using a survey data example. Keywords: synthetic data, disclosure control, CART, R, UK Longitudinal Studies. This introduction to the R package synthpop is a slightly amended version of Nowok B, Raab GM, Dibben C (2016). synthpop: Bespoke Creation of Synthetic Data in R. Journal of Statistical Software, 74(11), 1-26. doi:10.18637/jss.v074.i11. URL https://www.jstatsoft. org/article/view/v074i11. 1. Introduction and background 1.1. Synthetic data for disclosure control National statistical agencies and other institutions gather large amounts of information about individuals and organisations. Such data can be used to understand population processes so as to inform policy and planning. The cost of such data can be considerable, both for the collectors and the subjects who provide their data. Because of confidentiality constraints and guarantees issued to data subjects the full access to such data is often restricted to the staff of the collection agencies. Traditionally, data collectors have used anonymisation along with simple perturbation methods such as aggregation, recoding, record-swapping, suppression of sensitive values or adding random noise to prevent the identification of data subjects.
    [Show full text]
  • Bootstrapping Regression Models
    Bootstrapping Regression Models Appendix to An R and S-PLUS Companion to Applied Regression John Fox January 2002 1 Basic Ideas Bootstrapping is a general approach to statistical inference based on building a sampling distribution for a statistic by resampling from the data at hand. The term ‘bootstrapping,’ due to Efron (1979), is an allusion to the expression ‘pulling oneself up by one’s bootstraps’ – in this case, using the sample data as a population from which repeated samples are drawn. At first blush, the approach seems circular, but has been shown to be sound. Two S libraries for bootstrapping are associated with extensive treatments of the subject: Efron and Tibshirani’s (1993) bootstrap library, and Davison and Hinkley’s (1997) boot library. Of the two, boot, programmed by A. J. Canty, is somewhat more capable, and will be used for the examples in this appendix. There are several forms of the bootstrap, and, additionally, several other resampling methods that are related to it, such as jackknifing, cross-validation, randomization tests,andpermutation tests. I will stress the nonparametric bootstrap. Suppose that we draw a sample S = {X1,X2, ..., Xn} from a population P = {x1,x2, ..., xN };imagine further, at least for the time being, that N is very much larger than n,andthatS is either a simple random sample or an independent random sample from P;1 I will briefly consider other sampling schemes at the end of the appendix. It will also help initially to think of the elements of the population (and, hence, of the sample) as scalar values, but they could just as easily be vectors (i.e., multivariate).
    [Show full text]
  • A Survey on Data Collection for Machine Learning a Big Data - AI Integration Perspective
    1 A Survey on Data Collection for Machine Learning A Big Data - AI Integration Perspective Yuji Roh, Geon Heo, Steven Euijong Whang, Senior Member, IEEE Abstract—Data collection is a major bottleneck in machine learning and an active research topic in multiple communities. There are largely two reasons data collection has recently become a critical issue. First, as machine learning is becoming more widely-used, we are seeing new applications that do not necessarily have enough labeled data. Second, unlike traditional machine learning, deep learning techniques automatically generate features, which saves feature engineering costs, but in return may require larger amounts of labeled data. Interestingly, recent research in data collection comes not only from the machine learning, natural language, and computer vision communities, but also from the data management community due to the importance of handling large amounts of data. In this survey, we perform a comprehensive study of data collection from a data management point of view. Data collection largely consists of data acquisition, data labeling, and improvement of existing data or models. We provide a research landscape of these operations, provide guidelines on which technique to use when, and identify interesting research challenges. The integration of machine learning and data management for data collection is part of a larger trend of Big data and Artificial Intelligence (AI) integration and opens many opportunities for new research. Index Terms—data collection, data acquisition, data labeling, machine learning F 1 INTRODUCTION E are living in exciting times where machine learning expertise. This problem applies to any novel application that W is having a profound influence on a wide range of benefits from machine learning.
    [Show full text]
  • The Probability Lifesaver: Order Statistics and the Median Theorem
    The Probability Lifesaver: Order Statistics and the Median Theorem Steven J. Miller December 30, 2015 Contents 1 Order Statistics and the Median Theorem 3 1.1 Definition of the Median 5 1.2 Order Statistics 10 1.3 Examples of Order Statistics 15 1.4 TheSampleDistributionoftheMedian 17 1.5 TechnicalboundsforproofofMedianTheorem 20 1.6 TheMedianofNormalRandomVariables 22 2 • Greetings again! In this supplemental chapter we develop the theory of order statistics in order to prove The Median Theorem. This is a beautiful result in its own, but also extremely important as a substitute for the Central Limit Theorem, and allows us to say non- trivial things when the CLT is unavailable. Chapter 1 Order Statistics and the Median Theorem The Central Limit Theorem is one of the gems of probability. It’s easy to use and its hypotheses are satisfied in a wealth of problems. Many courses build towards a proof of this beautiful and powerful result, as it truly is ‘central’ to the entire subject. Not to detract from the majesty of this wonderful result, however, what happens in those instances where it’s unavailable? For example, one of the key assumptions that must be met is that our random variables need to have finite higher moments, or at the very least a finite variance. What if we were to consider sums of Cauchy random variables? Is there anything we can say? This is not just a question of theoretical interest, of mathematicians generalizing for the sake of generalization. The following example from economics highlights why this chapter is more than just of theoretical interest.
    [Show full text]
  • A First Step Into the Bootstrap World
    INSTITUTE FOR DEFENSE ANALYSES A First Step into the Bootstrap World Matthew Avery May 2016 Approved for public release. IDA Document NS D-5816 Log: H 16-000624 INSTITUTE FOR DEFENSE ANALYSES 4850 Mark Center Drive Alexandria, Virginia 22311-1882 The Institute for Defense Analyses is a non-profit corporation that operates three federally funded research and development centers to provide objective analyses of national security issues, particularly those requiring scientific and technical expertise, and conduct related research on other national challenges. About This Publication This briefing motivates bootstrapping through an intuitive explanation of basic statistical inference, discusses the right way to resample for bootstrapping, and uses examples from operational testing where the bootstrap approach can be applied. Bootstrapping is a powerful and flexible tool when applied appropriately. By treating the observed sample as if it were the population, the sampling distribution of statistics of interest can be generated with precision equal to Monte Carlo error. This approach is nonparametric and requires only acceptance of the observed sample as an estimate for the population. Careful resampling is used to generate the bootstrap distribution. Applications include quantifying uncertainty for availability data, quantifying uncertainty for complex distributions, and using the bootstrap for inference, such as the two-sample t-test. Copyright Notice © 2016 Institute for Defense Analyses 4850 Mark Center Drive, Alexandria, Virginia 22311-1882
    [Show full text]
  • Notes Mean, Median, Mode & Range
    Notes Mean, Median, Mode & Range How Do You Use Mode, Median, Mean, and Range to Describe Data? There are many ways to describe the characteristics of a set of data. The mode, median, and mean are all called measures of central tendency. These measures of central tendency and range are described in the table below. The mode of a set of data Use the mode to show which describes which value occurs value in a set of data occurs most frequently. If two or more most often. For the set numbers occur the same number {1, 1, 2, 3, 5, 6, 10}, of times and occur more often the mode is 1 because it occurs Mode than all the other numbers in the most frequently. set, those numbers are all modes for the data set. If each number in the set occurs the same number of times, the set of data has no mode. The median of a set of data Use the median to show which describes what value is in the number in a set of data is in the middle if the set is ordered from middle when the numbers are greatest to least or from least to listed in order. greatest. If there are an even For the set {1, 1, 2, 3, 5, 6, 10}, number of values, the median is the median is 3 because it is in the average of the two middle the middle when the numbers are Median values. Half of the values are listed in order. greater than the median, and half of the values are less than the median.
    [Show full text]
  • Sampling Student's T Distribution – Use of the Inverse Cumulative
    Sampling Student’s T distribution – use of the inverse cumulative distribution function William T. Shaw Department of Mathematics, King’s College, The Strand, London WC2R 2LS, UK With the current interest in copula methods, and fat-tailed or other non-normal distributions, it is appropriate to investigate technologies for managing marginal distributions of interest. We explore “Student’s” T distribution, survey its simulation, and present some new techniques for simulation. In particular, for a given real (not necessarily integer) value n of the number of degrees of freedom, −1 we give a pair of power series approximations for the inverse, Fn ,ofthe cumulative distribution function (CDF), Fn.Wealsogivesomesimpleandvery fast exact and iterative techniques for defining this function when n is an even −1 integer, based on the observation that for such cases the calculation of Fn amounts to the solution of a reduced-form polynomial equation of degree n − 1. We also explain the use of Cornish–Fisher expansions to define the inverse CDF as the composition of the inverse CDF for the normal case with a simple polynomial map. The methods presented are well adapted for use with copula and quasi-Monte-Carlo techniques. 1 Introduction There is much interest in many areas of financial modeling on the use of copulas to glue together marginal univariate distributions where there is no easy canonical multivariate distribution, or one wishes to have flexibility in the mechanism for combination. One of the more interesting marginal distributions is the “Student’s” T distribution. This statistical distribution was published by W. Gosset in 1908.
    [Show full text]
  • Common Data Set 2020-2021 University of Pennsylvania
    Common Data Set 2020-2021 University of Pennsylvania Table of Contents A General Information page 3 B Enrollment and Persistence 5 C First Time, First Year Admission 8 D Transfer Admission 14 E Academic Offerings and Policies 16 F Student Life 18 G Annual Expenses 20 H Financial Aid 22 I Instructional Faculty and Class Size 28 J Disciplinary Areas of Degrees Conferred 30 Common Data Set Definitions 32 Common Data Set 2020-21 1 25 Jun 2021 Common Data Set 2020-21 2 25 Jun 2021 A. General Information return to Table of Contents A1 Address Information A1 University of Pennsylvania A1 Mailing Address: 1 College Hall, Room 100 A1 City/State/Zip/Country: Philadelphia, PA 19104-6228 A1 Main Phone Number: 215-898-5000 A1 Home Page Address www.upenn.edu A1 Admissions Phone Number: 215-898-7507 A1 Admissions Office Mailing Address: 1 College Hall A1 City/State/Zip/Country: Philadelphia, PA 19104 A1 Admissions Fax Number: 215-898-9670 A1 Admissions E-mail Address: [email protected] A1 Online application www.admissions.upenn.edu A2 Source of institutional control (Check only one): A2 Public A2 Private (nonprofit) x A2 Proprietary A3 Classify your undergraduate institution: A3 Coeducational college A3 Men's college A3 Women's college A4 Academic year calendar: A4 Semester x A4 Quarter A4 Trimester A4 4-1-4 A4 Continuous A5 Degrees offered by your institution: A5 Certificate x A5 Diploma A5 Associate x A5 Transfer Associate A5 Terminal Associate x A5 Bachelor's x A5 Postbachelor's certificate x A5 Master's x A5 Post-master's certificate x A5 Doctoral degree - research/scholarship x A5 Doctoral degree - professional practice x A5 Doctoral degree - other x A5 Doctoral degree -- other Common Data Set 2020-21 3 25 Jun 2021 Common Data Set 2020-21 4 25 Jun 2021 B.
    [Show full text]
  • Lecture 14 Testing for Kurtosis
    9/8/2016 CHE384, From Data to Decisions: Measurement, Kurtosis Uncertainty, Analysis, and Modeling • For any distribution, the kurtosis (sometimes Lecture 14 called the excess kurtosis) is defined as Testing for Kurtosis 3 (old notation = ) • For a unimodal, symmetric distribution, Chris A. Mack – a positive kurtosis means “heavy tails” and a more Adjunct Associate Professor peaked center compared to a normal distribution – a negative kurtosis means “light tails” and a more spread center compared to a normal distribution http://www.lithoguru.com/scientist/statistics/ © Chris Mack, 2016Data to Decisions 1 © Chris Mack, 2016Data to Decisions 2 Kurtosis Examples One Impact of Excess Kurtosis • For the Student’s t • For a normal distribution, the sample distribution, the variance will have an expected value of s2, excess kurtosis is and a variance of 6 2 4 1 for DF > 4 ( for DF ≤ 4 the kurtosis is infinite) • For a distribution with excess kurtosis • For a uniform 2 1 1 distribution, 1 2 © Chris Mack, 2016Data to Decisions 3 © Chris Mack, 2016Data to Decisions 4 Sample Kurtosis Sample Kurtosis • For a sample of size n, the sample kurtosis is • An unbiased estimator of the sample excess 1 kurtosis is ∑ ̅ 1 3 3 1 6 1 2 3 ∑ ̅ Standard Error: • For large n, the sampling distribution of 1 24 2 1 approaches Normal with mean 0 and variance 2 1 of 24/n 3 5 • For small samples, this estimator is biased D. N. Joanes and C. A. Gill, “Comparing Measures of Sample Skewness and Kurtosis”, The Statistician, 47(1),183–189 (1998).
    [Show full text]
  • Data Analysis
    © Jones & Bartlett Learning, LLC. NOT FOR SALE OR DISTRIBUTION Chapter 13 Data Analysis James Eldridge © VLADGRIN/iStock/Thinkstock Chapter Objectives At the conclusion of this chapter, the learner will be able to: 1. Identify the types of statistics available for analyses in evidence-based practice. 2. Define quantitative analysis, qualitative analysis, and quality assurance. 3. Discuss how research questions define the type of statistics to be used in evidence-based practice research. 4. Choose a data analysis plan and the proper statistics for different research questions raised in evidence-based practice. 5. Interpret data analyses and conclusions from the data analyses. 6. Discuss how quality assurance affects evidence-based practice. Key Terms Analysis of variance (ANOVA) Magnitude Central tendency Mean Chi-square Median Interval scale Mode 9781284108958_CH13_Pass03.indd 375 10/17/15 10:16 AM © Jones & Bartlett Learning, LLC. NOT FOR SALE OR DISTRIBUTION 376 | Chapter 13 Data Analysis Nominal scale Quantitative analysis Ordinal scale Ratio scale Qualitative analysis Statistical Package for the Social Quality assurance Sciences (SPSS) Quality improvement t-test nnIntroduction This text methodically explains how to move from the formulation of the hypothesis to the data collection stage of a research project. Data collection in evidence-based practice (EBP) might be considered the easiest part of the whole research experience. The researcher has already formed the hypothesis, developed the data collection methods and instruments, and determined the subject pool characteristics. Once the EBP researcher has completed data collection, it is time for the researcher to compile and interpret the data so as to explain them in a meaningful context.
    [Show full text]